Fix64.csub: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix64.bend as Fix64
Lines 102-107 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix64.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix64.bend&start_line=102&end_line=107

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/generic.bend as SG
import bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend as SF
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/fixed.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend as G

def csub(+a: WU.U64, +b: WU.U64, +ok: Bool, +hok: {Nat.is_le(SG.u64_val(b), SG.u64_val(a)) == ok : Bool}) -> {SF.mval(~WU.U64, ~SG.u64_val, F.opt(WU.U64, X.lt(a, b), X.sub(a, b))) == SF.keep(ok, Nat.sub(SG.u64_val(a), SG.u64_val(b))) : Maybe<&2, Nat>}:
  match ok:
    case True{}:
      G.some_of(~WU.U64, ~SG.u64_val, X.lt(a, b), Equal.trans(Bool, X.lt(a, b), Nat.is_lt(SG.u64_val(a), SG.u64_val(b)), False{}, WA.lt_value(a, b), N.le_not_lt(SG.u64_val(a), SG.u64_val(b), hok)), X.sub(a, b), Nat.sub(SG.u64_val(a), SG.u64_val(b)), WA.sub_value(a, b, hok))
    case False{}:
      G.none_of(~WU.U64, ~SG.u64_val, X.lt(a, b), Equal.trans(Bool, X.lt(a, b), Nat.is_lt(SG.u64_val(a), SG.u64_val(b)), True{}, WA.lt_value(a, b), N.not_le_lt(SG.u64_val(b), SG.u64_val(a), hok)), X.sub(a, b))

Uses (20):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=le_not_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=not_le_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend&name=none_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend&name=some_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend&name=lt_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend&name=sub_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend&name=keep
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend&name=mval
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/generic.bend&name=u64_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/fixed.bend&name=opt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=sub